A simple and robust three-dimensional cracking-particle method without enrichment

Timon Rabczuk; Goangseup Zi; Stephane Bordas; Hung Nguyen-Xuan

doi:10.1016/j.cma.2010.03.031

A simple and robust three-dimensional cracking-particle method without enrichment

Timon Rabczuk, Goangseup Zi, Stephane Bordas, Hung Nguyen-Xuan

Research output: Contribution to journal › Article › peer-review

852 Citations (Scopus)

Abstract

A new robust and efficient approach for modeling discrete cracks in meshfree methods is described. The method is motivated by the cracking-particle method (Rabczuk T., Belytschko T., International Journal for Numerical Methods in Engineering, 2004) where the crack is modeled by a set of cracked segments. However, in contrast to the above mentioned paper, we do not introduce additional unknowns in the variational formulation to capture the displacement discontinuity. Instead, the crack is modeled by splitting particles located on opposite sides of the associated crack segments and we make use of the visibility method in order to describe the crack kinematics. We apply this method to several two- and three-dimensional problems in statics and dynamics and show through several numerical examples that the method does not show any "mesh" orientation bias.

Original language	English
Pages (from-to)	2437-2455
Number of pages	19
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	199
Issue number	37-40
DOIs	https://doi.org/10.1016/j.cma.2010.03.031
Publication status	Published - 2010 Aug

Bibliographical note

Funding Information:
The first author would like to thank the German Research Foundation (DFG) , Grant RA 1946/2-1 . The second author would like to thank the Agency for Defense Development (ADD) , Korea for Grant ADD-06-05-06 .

Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

Keywords

Cohesive crack model
Dynamic fracture
Meshfree methods

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
General Physics and Astronomy
Computer Science Applications

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10.1016/j.cma.2010.03.031

Cite this

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title = "A simple and robust three-dimensional cracking-particle method without enrichment",

abstract = "A new robust and efficient approach for modeling discrete cracks in meshfree methods is described. The method is motivated by the cracking-particle method (Rabczuk T., Belytschko T., International Journal for Numerical Methods in Engineering, 2004) where the crack is modeled by a set of cracked segments. However, in contrast to the above mentioned paper, we do not introduce additional unknowns in the variational formulation to capture the displacement discontinuity. Instead, the crack is modeled by splitting particles located on opposite sides of the associated crack segments and we make use of the visibility method in order to describe the crack kinematics. We apply this method to several two- and three-dimensional problems in statics and dynamics and show through several numerical examples that the method does not show any {"}mesh{"} orientation bias.",

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author = "Timon Rabczuk and Goangseup Zi and Stephane Bordas and Hung Nguyen-Xuan",

note = "Funding Information: The first author would like to thank the German Research Foundation (DFG) , Grant RA 1946/2-1 . The second author would like to thank the Agency for Defense Development (ADD) , Korea for Grant ADD-06-05-06 . Copyright: Copyright 2011 Elsevier B.V., All rights reserved.",

year = "2010",

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doi = "10.1016/j.cma.2010.03.031",

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AU - Rabczuk, Timon

AU - Zi, Goangseup

AU - Bordas, Stephane

AU - Nguyen-Xuan, Hung

N1 - Funding Information: The first author would like to thank the German Research Foundation (DFG) , Grant RA 1946/2-1 . The second author would like to thank the Agency for Defense Development (ADD) , Korea for Grant ADD-06-05-06 . Copyright: Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2010/8

Y1 - 2010/8

N2 - A new robust and efficient approach for modeling discrete cracks in meshfree methods is described. The method is motivated by the cracking-particle method (Rabczuk T., Belytschko T., International Journal for Numerical Methods in Engineering, 2004) where the crack is modeled by a set of cracked segments. However, in contrast to the above mentioned paper, we do not introduce additional unknowns in the variational formulation to capture the displacement discontinuity. Instead, the crack is modeled by splitting particles located on opposite sides of the associated crack segments and we make use of the visibility method in order to describe the crack kinematics. We apply this method to several two- and three-dimensional problems in statics and dynamics and show through several numerical examples that the method does not show any "mesh" orientation bias.

AB - A new robust and efficient approach for modeling discrete cracks in meshfree methods is described. The method is motivated by the cracking-particle method (Rabczuk T., Belytschko T., International Journal for Numerical Methods in Engineering, 2004) where the crack is modeled by a set of cracked segments. However, in contrast to the above mentioned paper, we do not introduce additional unknowns in the variational formulation to capture the displacement discontinuity. Instead, the crack is modeled by splitting particles located on opposite sides of the associated crack segments and we make use of the visibility method in order to describe the crack kinematics. We apply this method to several two- and three-dimensional problems in statics and dynamics and show through several numerical examples that the method does not show any "mesh" orientation bias.

KW - Cohesive crack model

KW - Dynamic fracture

KW - Meshfree methods

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ER -

A simple and robust three-dimensional cracking-particle method without enrichment

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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